Question: Simplify the following expression: $y = \dfrac{-72k - 36}{36k + 156}$ You can assume $k \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-72k - 36 = - (2\cdot2\cdot2\cdot3\cdot3 \cdot k) - (2\cdot2\cdot3\cdot3)$ The denominator can be factored: $36k + 156 = (2\cdot2\cdot3\cdot3 \cdot k) + (2\cdot2\cdot3\cdot13)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $y = \dfrac{(12)(-6k - 3)}{(12)(3k + 13)}$ Dividing both the numerator and denominator by $12$ gives: $y = \dfrac{-6k - 3}{3k + 13}$